Organizational Structure and Responsibility
Lamb
`
er Royakkers
1
, Davide Grossi
2
and Frank Dignum
2
1
Eindhoven University of Technology, The Netherlands
2
Utrecht University, The Netherlands
Abstract. We analyze the organizational structure of multi-agent systems and
explain the precise added value and the effects of such organizational structure
on the involved agents. To pursue this aim, contributions from social and organi-
zation theory are considered which provide a solid theoretical foundation to this
analysis. We argue that organizational structures should be seen along at least
three dimensions, instead of just one: power, coordination, and control. In order
to systematize the approach, formal tools are used to describe the organizational
structure as well as the effect of such structures on the activities in multi-agent
systems, and especially the responsibilities within organizations of agents. The
main aim of the research is to provide a formal analysis of the connections be-
tween collective obligations to individual responsibilities. Which individual agent
in a group should be held responsible if an obligation directed to the whole group
is not fulfilled? We will show how the three dimensions of an organizational
structure together with a specific task decomposition determine the responsibili-
ties within a (norm-governed) organization.
1 Introduction
The concept of responsibility is a central concept to all legal systems and norm-governed
organizations. Analyzing this concept is therefore fundamental if we aim at improving
the behavior of these systems or organizations. Obtaining a formal representation of
responsibility, however, is quite complex because of the very different meanings of this
concept can take. Our concept of responsibility is restricted to the analysis of organiza-
tional performance. Therefore, we clarify and classify some meanings of responsibility
and we relate them to the three relevant dimensions of an organizational structure we
isolated in [1]. These three relevant dimensions are power, coordination and control,
with their matching actions ’to delegate’, to inform’ and ’to monitor’. The coordi-
nation actions are actually only one type of meta actions that should be considered.
Besides the plan to achieve the content of the obligation the group should create that
plan, allocate agents to parts of the plan, create a plan for what to do when the original
plan fails, etc. These meta actions should also be coordinated again creating in the end
an infinite regression of meta actions. In this paper we will not take all these layers into
account, but will limit us to the coordination actions that are necessary to indicate the
several notions of responsibility.
In this article we will import some of the studies in organizations and social theory
to describe a more rigorous foundation of organizational structures in MAS, which will
Royakkers L., Grossi D. and Dignum F. (2006).
Organizational Structure and Responsibility.
In Proceedings of the 3rd International Workshop on Computer Supported Activity Coordination, pages 65-74
DOI: 10.5220/0002482000650074
Copyright
c
SciTePress
be informally and formally exposed in Section 2. In order to describe organizational
structures we have to first describe exactly what the meaning is of the relations that
form the structure. E.g. what is the meaning of an “power” relation and, maybe even
more importantly, what are the consequences of the existence of such a relation between
two agents? We will introduce a modal logic for this characterization. Several notions of
responsibility (given a plan) will be discussed formally in Section 3. How the individual
responsibilities relate to the underlying structure of an organization will be discussed
in Section 4. In the last section, we will draw some conclusions and give directions for
future research.
2 Organizational Structure and its Logic
The thesis we hold in this paper, which is inspired by foundational work on social and
organization theory like [2–5], is that organizations do not exhibit one single structural
dimension, but that they are instead multi-structured objects. In particular, we view or-
ganizational structure as hiding at least three relevant dimensions which we call: power,
information and control. We will analyze power in relation with the delegation activity,
coordination in relation with the knowledge and information issues, and control in re-
lation with the monitoring and recovery issues. As a result of this analysis, organizations
will be represented as explicitly displaying a triple structure constrained on the basis of
the interplay between the three notions of power, coordination, and control. It is the
structure based on goal or task decomposition and related to power and delegation ca-
pabilities between the roles. Although we do not pretend to give full definitions of these
relations (see [6,7] for some more elaborate definitions of the delegation and power
relations) we will characterize these relations in terms of some of their consequences
for the agents, enacting the roles, between which these relations are defined.
To describe an organization and its structure we will use a (typed) multi-modal
propositional logic. The organizational structures are denoted through the special propo-
sitions Power(r, s) to indicate that ‘the agent enacting role r has the agent enacting role
s in its power’ (i.e. the agent playing role r can delegate goals to the agent playing role
s), Coordination(r, s) to indicate that ‘the agent enacting role s has access to the in-
formation that is accessible to the agent enacting role r’, and Control(r, s) to indicate
that ‘the agent enacting role r controls the agent enacting role s’ (i.e. the agent playing
role r is responsible for the agent playing role s). Note that these relations are defined
on roles. We denote the fact that agent i enacts role r, i.e., is a role enacting agent
([8]), by the special proposition rea(i, r). Furthermore we use a modal operator K
i
for
knowledge accessible to an agent i. For the characterization of the organization struc-
tures we build on dynamic logic ([9]). Dynamic formulas such as [ξ]φ, meaning that
after each execution of ξ formula φ holds, where ξ is a parameterized construct of the
type i : α denoting the performance of action α by agent or role i, or a composed
construct such as: i : α
1
; j : α
2
(subsequent performance), i : α
1
&j : α
2
(parallel
performance),
i : α (i refrains from performing α). The formal semantics is given by
means of a Kripke structure where there are accessibility relations R
i:α
associated with
each parameterized action i : α.
66
We can now give a full formal definition of the syntax of our description language
Org:
Definition 1. (Syntax of Org)
Given a finite set AR of role names, a finite set Ag of agent names, a countable set P
0
of atomic propositions, a finite set of parameterized actions A (in general the elements
of A are denoted by i : α with i in Ag the performing agent of α) containing at least i :
achieve(φ), i : delegate(j, φ), i : inform(j, φ) and i : monitor(φ), the propositional
language L
p
that is built up from atoms P
0
, the countable set P = L
p
{Power(r, s),
Coordination(r, s), Control(r, s), rea(i, r) | r, s AR, i Ag, φ L
p
}, the
admissible formulas are recursively defined as follows:
P Org
If φ and ψ Org, then φ ψ, ¬φ Org
If φ Org and i A, then K
i
(φ) Org
If φ Org and i : α A, then [i : α]φ Org
If i : α A, then DON E(i : α), DO(i : α), O(i : α) and Can(i : α) Org
Binary connectives and , and nullary connective can be defined as usual. For
the knowledge operators (K
i
) we assume the axiomatization characterizing S5. The
assertions DONE(i : α) stands for α has just been performed by agent i”, DO(i : α)
stands for α is going to be the next action performed by agent i”, and CAN
i
(α)) stands
for “α lies in the capabilities of agent i”. O(i : α) is the deontic assertion to the effect
that agent i ought to perform action α.
The semantics of Org will be given in two steps. First we define the semantics of the
special relations Power , Coordination and Control through a multi-digraph defined
on the set of roles. This defines a tuple OS which will be part of the Kripke model
given after. We will only introduce some basic elements which are strictly of use for the
development of this article.
Definition 2. (Organizational structures)
OS is characterized by the following:
hRoles Agents, {R
P ower
, R
Coordination
, R
Control
, Rea}i
where Roles Agents is the finite set of roles and agents;
and {R
P ower
, R
Coordination
, R
Control
} are three irreflexive binary relations on Roles
characterizing the Power, Coordination and Control structures. Rea indicates which
agents play which roles.
The semantics of Org is defined in terms of Kripke models (cf. [1]).
3 A Formal Analysis
3.1 Task Allocation
In order for organizations to fulfill their objectives, subtasks are isolated via a form of
organizational planning and distributed in a way which defines the roles agents can play
67
in contributing to the performance of the organization. We call this designing process
of the activity of an organization task-allocation. Roles can then be seen as sort of
placeholders in a rationally designed activity of an organizations: an agent taking part
to the organization will occupy one of these places, that is, will play a role. In this work,
agents playing a role in an organization are called, following [8], role enacting agents
or reas.
The distribution of the sub-tasks in an organization in order to achieve a certain
goal or collective task τ depends on a plan of the organization, i.e., a concrete manner
to achieve the goal (collective task). We can define a plan to achieve a certain goal
τ as a decomposition of the complex action achieve(τ ) by a sequence of (possible
simultaneous) individual actions. Besides task division, task allocation is needed, which
indicates which role of the organization has to achieve which sub-task of the complex
task. We use the following definition for task allocation:
Definition 3. (Task allocation)
A task allocation for a task τ within the set of roles AR is defined as follows:
hr
1
: achieve(τ
1
) r
2
: achieve(τ
2
) . . . r
n
: achieve(τ
n
)i
such that r
1
: achieve(τ
1
)r
2
: achieve(τ
2
). . .r
n
: achieve(τ
n
)]τ. We refer to the
task allocation of τ within AR as P lan(AR, τ ). To indicate that task achieve(τ
j
) has
been allocated to role r
j
in P lan(AR, τ) (for j = 1, 2, . . . , n), we use the following
notation: hr
j
: τ
j
i P lan(AR, τ)
3
.
where stands for either the simultaneous operator & or the sequential operator
’;’. r
1
: achieve(τ
1
)&r
2
: achieve(τ
2
) stands for the simultaneous performance of
achieve(τ
1
) by an agent enacting role r
1
and achieve(τ
2
) by an agent enacting role
r
2
, and r
1
: achieve(τ
1
); r
2
: achieve(τ
2
) stands for the sequential composition of
r
1
: achieve(τ
1
) and r
2
: achieve(τ
2
).
We need the simultaneous operator, since some actions have to be performed at the
same time. The sequential operator is needed because some actions might depend on
other ones: a certain action can only be performed if an other action is done. So, the
plan must at least determine the order of sub-actions. For example, the notification of
acceptance of a certain paper by an Editorial Board can only be done if it is reviewed
by some members of the Editorial Board.
We will use the concept of task allocation as a starting point for framing the various
notions we are interested in. In particular, as we will see in the coming section, it plays
an essential role for the definition of the notion of task-based responsibility. Besides,
we will analyze the notion of “failure” in the accomplishment of a task understanding
it as an organizational variant of the notion of social harm described in [10]. In our
context, we define the untoward event Dτ
r
as the impossibility, or the reduction of the
possibility to achieve the goal τ allocated to role r. The performance of an action α by
an agent i enacting role r determining social harm can then be represented as [i : α]Dτ
r
,
that means, after each execution of action α by agent i the social harm represented by
Dτ
r
is the case.
3
Note that the function of the numeric index j consists in denoting the position within the task
allocation sequence.
68
3.2 Responsibilities in Form
So far we have dealt with organizations at their role level, where the task-allocation and
the organizational structure range. Responsibilities concern agents and arise in relation
with task-allocation and structure once there are agents enacting the roles of a given
organization.
Given a task-allocation allocating a specific subtask to a role, and given that an agent
is enacting that role, the agent is then said to be responsible for that task or task-based
responsible. In other words, the allocation of subtasks to roles determines a distribution
of what we call task-based responsibilities over the set of agents enacting the roles
of the organization. Being autonomous, agents can independently decide whether to
perform the subtasks to which they are allocated or not, and whether to perform them
in the expected way. In this case the fulfillment of the organizational objectives is put
in jeopardy by the conduct of some agent that is said then to be causally responsible for
the failure occurred.
In organizations an agent can happen to be causally responsible of some failure
without actually being blamed by the organization. This can happen if an agent i which
is task-based responsible for performing a task, delegates the performance to a sub-
ordinate agent j which fails or jeopardizes the execution of the delegated task. This
observation reveals an interplay between the notions of responsibility isolated above,
and dimensions of social structure such as the possibility to delegate allocated tasks,
i.e., what we called power relation in the previous section. Social structure in relation
with responsibility will be discussed in detail in Section 4. Here it suffices to notice that
the presence of a power structure within an organization causes a difference between
the two notions of task-based and causal responsibility: ‘I may have not performed the
task you delegated to me, but you were the one appointed to it’. Therefore, if an orga-
nizational task is not performed, the one being socially responsible in front of the orga-
nization, the one who gets the blame for the failure, is not necessarily the one causally
responsible for it, but it is the one to which that task was appointed. The acknowledg-
ment of such a gap calls for the distinction of yet another meaning of the notion of
responsibility which we call failure-based responsibility: who should control the per-
formance of an agent to check whether a failure occurs and take countermeasures if that
is the case?
We can now provide an action logic representation of the notions of responsibility.
Causal responsibility.
An agent is said to be causally responsible when it does something (or fails to do some-
thing) that causes the untoward event D
τ
. We formalize causal responsibility as follows:
Definition 4. (Causal responsibility)
For all i Ag: R
c
i
(Dτ) := [i : α]Dτ DO(i : α) ¬
meaning that agent i is causally responsible for the untoward event if and only if agent i
performs an action which necessarily determines the occurrence of the untoward event
and, finally, the untoward event is not the case before the agent performs the action.
Causal responsibility can also be attributed to nonhuman events, for example, that
a house is severely damaged in a storm. In this article, we restrict ourselves to agents
69
in an organizational context. Notice that an agent which is causally responsible, may
not be considered blameworthy. For example, if the chairman of the Editorial Board
has forgotten to inform a member i to review some papers in one week, and agent i did
not review the papers in one week, then the achievement of the goal of the Editorial
Board to notify of the results of the reviews within the deadline will be reduced. The
member i would be considered responsible in the sense of having caused the situation,
but he would not be responsible in the sense of blameworthy. An agent does something
blameworthy, if he knows (or could have known) that the action he performs leads to
the impossibility or the reduction of the possibility to achieve a goal τ:
Definition 5. (Causal blameworthiness)
For all i Ag: Bl
c
i
(Dτ) := [i : α]Dτ DO(i : α) ¬ K
i
([i : α] )
The importance of the knowledge component in the dynamics of responsibilities within
organizations is analyzed in detail in Section 4.
Task-based responsibility.
The notion of task-based responsibility is somehow interchangeable with duty and
refers to what individuals are expected to do in virtue of their social roles. We as-
sume that task-based responsibility is a consequence of role adoption: an agent who
accepts to play a given role in an organization takes a responsibility with regard to the
accomplishment of that role, i.e., with the tasks associated to it [10]. In this article, this
notion of responsibility completely depends on the position an agent occupies in the
performance of the organization.
Definition 6. (Task-based responsibility)
For all i Ag and a task allocation P lan(AR, τ ):
R
tb
i
(τ
j
) := rea(i, r
j
) hr
j
: τ
j
i P lan(AR, τ)
Intuitively, we want that the following property holds:
Property 1. For all i, j Ag and a task allocation P lan(AR, τ ):
R
tb
i
(τ
j
) O(i : achieve(τ
j
)) [
i : achieve(τ
j
)]Dτ
j
The obligation O(i : achieve(τ
j
)) expresses that the organization entrusts agent i
with his task τ
j
(rea(i, r
j
) hr
j
: τ
j
i P lan(AR, τ)), and [i : achieve(¬τ
j
)]Dτ
j
expresses the empowerment of i to prevent the reduction of the possibility or the im-
possibility to achieve goal τ
j
. So, an agent i fails to fulfill his task-based responsibility
R
tb
i
(τ
j
) if he violates the norm O(i : achieve(τ
j
)) which leads to the untoward event
Dτ
j
. However, the agent is considered blameworthy when he actually knows (or could
have known) that he has this obligation and that he can perform the action to achieve
his task. For example, he has not received the information needed for the performance
of his task, or the achievement of his task depends on an earlier task in the task alloca-
tion which is not performed. This notion of blameworthy can formally be described as
follows:
70
Definition 7. (Task-based blameworthiness)
For all i Ag and a task allocation P lan(AR, τ ):
Bl
tb
i
(τ
j
) := R
tb
i
(τ
j
) K
i
(R
tb
i
(τ
j
)) CAN
i
(achieve(τ
j
))
Social responsibility.
The notion of social responsibility builds on the notion of task-based responsibility, and
it is somehow analogous to a notion of violation in standard deontic logic.
Definition 8. (Social responsibility)
For all i Ag and a task allocation P lan(AR, τ ): R
s
i
(τ
j
) := R
tb
i
(τ
j
) D
τ
j
that is to say, agent i has the responsibility to achieve τ
j
and the achievement of τ
j
is
impossible or jeopardized. Notice that this notion of responsibility is very simple and is
independent from the notion of causal responsibility.
4 Responsibilities and Organization Structure
We cannot hope to provide a full account of all interactions between responsibilities
and organizational structures. However, in the rest of this section we aim to capture
some essential traits of those interconnections. We understand those relations essen-
tially as guaranteeing some effects to the basic actions of delegate, inform and monitor,
which play an essential role with respect to responsibilities and their development in
organizations.
The following definitions characterize the influence of the organization relations on
the actions above. Through these basic properties we can also formally analyze some
consequences of them on the notions of responsibilities studied in the previous section.
Definition 9. (Power)
For all i, j Ag s.t. i 6= j and r, s AR:
(Power(r, s) rea(i, r) rea(j, s)) [i : delegate(j, φ)]O(j : achieve(φ))
If a power relation exists between roles that are enacted by two agents then a delegate
action will have as effect an obligation for the recipient, that is, a form of “your wish
is my command” principle. Intuitively, if a power relation holds between roles r and
s, all delegation acts performed by an agent i enacting role r on agents enacting role s
succeed in creating an obligation for these agents.
Task-based responsibility cannot be delegated. If Agent i has, according the task
allocation, to achieve task φ and has a power relation with agent j, he can delegate his
task to j, but he remains task-based responsible for the achievement of φ. Since φ is
not the original task of agent j according to the given task allocation (see definition
6). Agent j, however, can be causally responsible if he fails to fulfill his delegated
obligation.
A difference between an individual task and a collective task is that in an individual
task all information is readily available and can be reasoned about. However, when a
collective task is divided over the individuals of that collective, they might not know
the whole plan, typically do not have information about actions that are performed, etc.
Therefore, we need a coordination structure.
71
Definition 10. (Coordination)
For all i, j Ag s.t. i 6= j, r, s AR:
((Coordination(r, s) rea(i, r) rea(j, s)) DON E(i : monitor(φ)))
((K
i
φ O(i : inform(j, φ))) [i : inform(j, φ)]K
j
φ)
If a coordination relation holds between roles r and s, all information acts performed
by agents enacting role r to agents enacting role s are successful in the sense that they
create, in these last agents, the knowledge they acquired via monitoring the occurrence
of a certain fact: the inform action will automatically lead to the corresponding epis-
temic state in the recipient. Further, there is a normative aspect: agent i should inform
another agent j about φ if they are connected through a coordination link and if agent i
has monitored (checked) φ.
On this basis, a coordination-related type of responsibility can be defined.
Definition 11. (Coordinational responsibility)
For all i, j Ag and a task allocation P lan(AR, τ ):
R
coor
i
(inform(j, φ)) := K
i
([
i : achieve(K
j
φ)]Dτ
l
) R
tb
j
(τ
l
)
On the basis of the coordination structure, there is a specific allocation of the infor-
mation actions, which is needed for the achievement of the individual tasks in the task
allocation. Given this definition, we can say agent i is responsible to inform agent j,
when the knowledge of φ is a necessary means to the achievement of τ
l
and that agent
j does not have that knowledge.
We state the if someone is coordinationally responsible to inform an agent about
φ, he is also obliged that the agent will be informed about φ. This can be expressed as
follows:
Property 2. For all i, j Ag and a task allocation P lan(AR, τ ):
R
coor
i
(inform(j, φ)) O(i : achieve(K
j
, φ))
The responsibility of an agent i to inform some agent j about a certain aspect φ can
follow from the coordination link between these agents if the knowledge of φ is neces-
sary for the achievement of the task of agent j according the task allocation and i can
monitor or check φ. This shows, in particular, how a given task allocation needs to be
integrated with a suitable allocation of coordinational responsibilities in order to guar-
antee the information necessary for the correct functioning of the organization. This
property can be formalized as follows:
Property 3. For all i, j Ag s.t. i 6= j, r
k
, r
l
AR and task allocation P lan(AR, τ ):
Coordination(r
k
, r
l
) rea(i, r
k
) rea(j, r
l
) hr
l
: τ
l
i P lan(AR, τ)
(¬K
j
φ ¬CAN(j : achieve(τ
l
))) CAN (i : monitor (φ)) R
coor
i
(inform(j, φ))
72
So, agent i is responsible to inform agent j about φ if there is a coordination link
between the roles r
l
and r
k
they respectively enact, and without the information about
φ agent j cannot perform his task according to the task allocation. If agent i does not
inform agent j, it follows that agent j cannot perform his task, which can lead to Dτ
l
.
So, agent i can be causally responsible if he does not inform agent j about φ (see
definition 4). Note, that agent j is still task-based responsible with respect to τ
l
, but not
blameworthy, when he does not get the information necessary for the achievement of τ
l
(see definition 7).
Finally, we get to a characterization of the dimension of control in organizational
structure:
Definition 12. (Control)
For all i, j Ag s.t. i 6= j and r
k
, r
l
AR:
(Control(r
k
, r
l
) rea(i, r
k
) rea(j, r
l
))
[i : monitor (DONE(j : achieve(φ))](Dτ
l
O(i : achieve(τ
l
))
If a control relation exists then the monitor action will have as further consequence the
generation of an obligation for the controller in case the controlled actor did not achieve
the relevant state causing the untoward event. On this basis, the notion of failure-based
responsibility can be defined.
Definition 13. (Failure-based responsibility)
For all i, j Ag s.t. i 6= j and r, s AR:
R
control
i
(monitor(j, φ)) := Control(r, s) rea(i, r) rea(j, s)
This type of responsibility depends completely on the control relation.
The control responsibility has another normative aspect: if an agent has control
over another agent he is obliged to monitor the controlled agent whenever he knows the
controlled agent has an obligation. Formally,
Property 4. For all i, j Ag and a task allocation P lan(AR, τ ):
(R
control
i
(monitor(j, φ)) K
i
(O(j : achieve(φ)))
O(i : monitor (DON E(j : achieve(φ))))
We can imagine that an agent who has delegated his task to agent j, has the obligation
to monitor whether the delegated agent has done the task, since he might be responsible
to monitor agent j and he knows that the delegated agent j has the obligation.
5 Conclusions
We have provided some elementary notions of responsibility in its interconnection with
the structure of an organization. We argued that organizations are defined through sev-
eral structural relations. Although people refer to these structures they still lack a precise
formal definition. In this article these relations have been given a solid foundation. This
73
allows us to check desirable properties of the structures and how they (should) interact.
Now we have a characterization and can proof properties given some structural proper-
ties of these relations. In future work we will look at more elaborate definitions of the
power, coordination and control relations.
Responsibilities are closely related to the specific task allocation within an organi-
zation. Although the task allocation can be determined dynamically through the process
of delegation, some of it is predetermined through the role structure of the organization
which assigns typical tasks to certain roles. The organizational structure plays an even
greater role in the monitoring and control of execution of the tasks for which the agents
are responsible. The logical framework we presented offers a semantics for the notions
of responsibility that is necessary for determining at least some interconnections be-
tween organizational structure and responsibilities. It gives some insides into when an
agent can really be held responsible for when tasks are not (or wrongly) performed.
These observations might lead to guidelines for the design of an organizational struc-
ture given that one wants some responsibilities to be covered at all times. In this article
we just offered a glance of these observations through the example. However, we hope
to extend this area in future work, e.g., to combine our work with the work done in [11]
about the representation of organized interaction with action concepts.
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